Two-dimensional Dirac operator and surface theory

Abstract

We give a survey on the Weierstrass representations of surfaces in three- and four-dimensional spaces, their applications to the theory of the Willmore functional and on related problems of spectral theory of the two-dimensional Dirac operator with periodic coefficients.

82 pages, minor additions

Cited by in corpus (3)

• Infinitesimal Darboux transformations of the spectral curves of tori in the four-space
• Nonlinear Dirac equations on Riemann surfaces
• Surfaces of revolution in the Heisenberg group and the spectral generalization of the Willmore functional